Wind Regimes - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 16

deviation from a height-independent geostrophic wind can give an additional
contribution to the vertical wind profile as well. The horizontal pressure gradient
becomes height-dependent in an atmosphere with a large-scale horizontal tem-
perature gradient. Such an atmosphere is called baroclinic and the difference in the
wind vector between geostrophic winds at two heights is called thermal wind. The
real atmosphere is nearly always at least slightly baroclinic, thus the thermal wind
is a general phenomenon.
Thermal winds do not depend on surface properties. So they can appear over all
surface types addressed in Chaps. 3 - 5 .
Differentiation of the hydrostatic equation ( 2.1 ) with respect to y and differ-
entiation of the definition equation for the u-component of the geostrophic wind
( 2.5 ) with respect to z leads after the introduction of a vertically averaged
temperature T M to the following relation for the height change of the west-east
wind component u:

o u

oz ¼ g

o T M
oy

ð 2 : 10 Þ

fT M

Subsequent integration over the vertical coordinate from the roughness length
z 0 to a height z gives finally for the west-east wind component at the height z:
u ð z Þ¼ u ð z 0 Þ g ð z z 0 Þ
fT M

o T M
oy

ð 2 : 11 Þ

The difference between u(z) and u(z 0 ) is the u-component of the thermal wind.
A similar equation can be derived for the south-north wind component v from Eqs.
( 2.1 ) and ( 2.6 ):

v ð z Þ¼ v ð z 0 Þþ g ð z z 0 Þ
fT M

o T M
ox

ð 2 : 12 Þ

Following ( 2.10 ) and ( 2.11 ), the increase of the west-east wind component with
height is proportional to the south-north decrease of the vertically averaged
temperature in the layer between z 0 and z. Likewise, ( 2.12 ) tells us that the south-
north wind component increases with height under the influence of a west-east
temperature increase. Usually, we have falling temperatures when travelling north
in the west wind belt of the temperate latitudes on the northern hemisphere, so we
usually have a vertically increasing west wind on the northern hemisphere.
Equations ( 2.11 ) and ( 2.12 ) allow for an estimation of the magnitude of the
vertical shear of the geostrophic wind, i.e. the thermal wind from the large-scale
horizontal temperature gradient. The constant factor g/(fT M ) is about 350 m/(s K).
Therefore, a quite realistic south-north temperature gradient of 10 -5 K/m (i.e.,
10 K per 1,000 km) leads to a non-negligible vertical increase of the west-east
wind component of 0.35 m/s per 100 m height difference.
The thermal wind also gives the explanation for the vertically turning winds
during episodes of cold air or warm air advection. Imagine a west wind blowing
from a colder to a warmer region. Equation ( 2.12 ) then gives an increase in the